Answer:
- rotate CCW 90°, reflect across the x-axis
- (x, y) ⇒ (-y, -x) . . . . . both transformations together
Step-by-step explanation:
The vertex order ABC is clockwise in the original figure and also in the first image: A'B'C'. The altitude from AC to B is up in the original and left in the first image, indicating a rotation 90° CCW.
The first transformation is a rotation 90° CCW.
The vertex order of A''B''C'' is CCW, indicating a reflection. The direction of the altitude from A''C'' to B'' is still to the left, so the reflection must be over a horizontal line. We find the x-axis bisects the segments A'A'', B'B'', and C'C'', confirming that it is the line of reflection.
The second transformation is reflection across the x-axis.
_____
Algebraically, the transformations are ...
1st: (x, y) ⇒ (-y, x)
2nd: (x, y) ⇒ (x, -y)
Both together: (x, y) ⇒ (-y, -x).
Answer:
0.3557 = 35.57% probability that one selected subcomponent is longer than 118 cm.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of 116 cm and a standard deviation of 5.4 cm.
This means that 
Find the probability that one selected subcomponent is longer than 118 cm.
This is 1 subtracted by the pvalue of Z when X = 118. So



has a pvalue of 0.6443
1 - 0.6443 = 0.3557
0.3557 = 35.57% probability that one selected subcomponent is longer than 118 cm.
we can multiply the equation with the invers of that fraction
Answer:
B
Step-by-step explanation:
Had it on Khan Academy.
Answer:
graph of function f of x equals 30 multiplied by 0.88 to the power of x
Step-by-step explanation:
The deodorant is begun to evaporate in other words, it is losing mass so the rate of 12% is a decay rate. In the exponential decay, the graph of the function goes according to the formula:

Where
is the initial amount (
),
is the rate of decay (
) and
the times intervals, in this case, measured in days. Substituting the values in the formula:

Which corresponds with the "graph of function f of x equals 30 multiplied by 0.88 to the power of x".